In Desktop Dungeon is it possible to beat Frank the Zombie with a Tier 1 Character? With 200+hp and a high attack I don't think I can beat him even with a lv 10 fighter with a save.
As one of the first bosses you have access to in the game, he's very much beatable by first tier classes.
You just need to plot out your resources properly. Frank has no tricks other than his high HP, so the solution is maximize your damage to him for each of your assaults.
One big thing you might consider is mid-battle leveling. In essence, leveling in the middle of a fight to restore health and mana by killing other enemies. Of the 1st tier classes, Fighters and Priests do pretty well in your first runs. Fighters get extra experience that makes it easier to setup, while Priests do extra damage to Undead. As it were, Frank is actually easier to face when you're a lower level and can make some level ups.
You can't poison Frank, because of his being Undead, so the main alternatives to keeping his HP low is to rely a lot on spells like BURNDAYRAZ and BYSSEPS to maximize the damage you deal before going to heal. Make every point of Mana count, don't use any exploration or potions that would waste any point of Mana. When you're not relying on potions, you just need to setup a rhythm so that you deal significantly more damage than he does, so that you don't have to punch through it all again as you heal up.
Item luck doesn't really figure in as much. Aside from poison and Frank being undead, almost everything you can find in a shop will benefit you in some fashion. I've also found that you don't really need much divine intervention, but please don't pick up Dracul.
Let's just put down some strategies overall for those 4 Tier 1 classes, eh?
Human probably represents your best bet, you can easily get a monstrous amount of attack without needing to worry too much for spells. The main setup is to use your extra experience and ability to see monsters to setup two or more mid-battle level ups for taking down Frank. Kill mid-level foes, probably just one step above you. Convert most glyphs, though BURNDAYRAZ doesn't hurt to have just for the extra damage. The attack power you should have in the end, though, should make mincemeat out of Frank without even needing the spells (Taurog, thus, is nice).
You want BURNDAYRAZ. Halfling/Gnome is much more common, but Elf isn't unheard of. Your dual-potion ability makes it much more potent to mix in BURNDAYRAZ with normal attacks. Simply attack, blast him with spells, then drink up. You should have more than enough potions on account of your Thief nature and race to simply outlast Frank, perhaps even around level 7 or 8.
A human priest actually works pretty well, because Frank presents an excellent target for a physical priest play. You deal double damage, you get extra health per level, and to top it off you only need a single health potion to get back to full health. This makes it pretty reasonable to simply boost your attack power so that he is crushed beneath your mighty weapon. No harm in taking him on late, with this kind of setup.
You could play Elf or Gnome, or you could play a Human to overtake your innate penalty. You probably want to setup some mid-battle levels that you can accomplish with melee attacks, so that you can spend all of your mana directly towards blasting Frank with BURNDAYRAZ. This probably represents the hardest of the 4, if only because the other 3 simply have greater advantages against this simply powerful zombie.